Is there any open software to provide cloud rendering via P2P?
There are Blender render farm services similar to folding@home: (Anyone can volunteer their computer time; the work is done and sent to a main server for collection by the project submitter.)


BURP - Big and Ugly Rendering Project
http://www.renderfarm.fi/‎
http://www.renderweb.org/RenderWeb/index.jsp (Inactive?)
http://www.vswarm.com/ (messages in forum saying that it appears to be abandoned.)


The list of blender farms I found these on, that also includes normal payed and free render farm services.

(I did not find any that are strictly P2P though. The ones I found are master-slave, but such a setup can be considered "cloud" too, (meaning computers on the internet are doing work for you) but one of them-- the master/main server is in charge of managing the workers and jobs.  A headless P2P distributed farm, like bitcoin or something is likely possible, but is perhaps more complicated than it's worth for now.) 

Concerns from ideasman42's answer do apply though, especially privacy.

There are also tools for building your own private distributed render farm: (These can be setup on spare machines, cloud/vps servers...)


http://brender-farm.org (thanks Gwenn)
BURP can also be used as a private render farm. (thanks jesterKing)
"Render: Network Render" A network rendering plugin included with Blender, with farm management tools. Video tutorial on how to set it up.
More listed in this answer by Aldrik